What is the answer?
What is the gradient of the blue line?

The expression used for finding the circumference of the circular pond is; C = 2π(d/2) feet.

For the given question;

Let 'd' be the diameter of the circular pond.

The diameter of the pond  = 15 feet.

Let 'C' be the circumference of the circle;

The, the formula for finding the circumference of the circle is;

C = 2π(d/2) feet

For, d = 15 feet

C = 2π(15/2) feet

Take π = 3.14

C = 2×3.14×(15/2) feet

C = 47.1 feet

Thus, the circumference of the circular pond is found as 47.1 feet.

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the algebraic expression is

the factor of the expression that is a sum is

Answer:

A. 15: 1, 3, 5, 15

20x: 1, 2, 4, 5, 10, 20, x

Step-by-step explanation:

Note: It the given equation the coefficient of \(x^2\) must be -16 instead of 16.

Given:

Consider the height  of the water balloon over  time can be modeled by the  function

\(y=-16x^2+160x+50\)

To find:

The maximum height of the water balloon  after it was thrown.

Solution:

We have,

\(y=-16x^2+160x+50\)

Here, leading coefficient is negative. So, it is a downward parabola and vertex of a downward parabola, is the point of maxima.

If a parabola is \(f(x)=ax^2+bx+c\), then

\(Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)\)

Here, \(a=-16,b=160,c=50\). So,

\(-\dfrac{b}{2a}=-\dfrac{160}{2(-16)}\)

\(-\dfrac{b}{2a}=-\dfrac{160}{-32}\)

\(-\dfrac{b}{2a}=5\)

Now, put x=5 in the given equation.

\(y=-16(5)^2+160(5)+50\)

\(y=-16(25)+800+50\)

\(y=-400+850\)

\(y=450\)

The vertex of the given parabolic equation is (5,450).

Therefore, the maximum height of the balloon is 450 units after 5 units of time.

In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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Steps to solve:

x² = 25

~Take the square root of both sides

x = ±5

Best of Luck!

Answer:

\(\large\boxed{x=5}\)

Step-by-step explanation:

\(x^{2}\) = 25

Find the square root of 25 to find the value of x (get rid of the exponent).

\(\sqrt{25}\) = 5

\(\large\boxed{x = 5}\)

Hope this helps :)

Yes, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

Here,

The differential equation (1-xy)y' = y^2

And,  y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2.

What is Differential equation?

A differential equation is a mathematical equation that relates some function with its derivatives.

Now,

To show y = e^xy is an implicit solution of the differential equation

(1-xy)y'=y^2, we have to find the solution of differential equation.

The differential equation is;

\((1-xy)y'=y^2\\\\\\\\\)

\((1-xy) \frac{dy}{dx} = y^2\)

\(\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }\)

It is form of  \(\frac{dx}{dy} + Px = Qy\),

Where, P is the function of y and Q is the function of x.

Hence, Integrating factor = \(e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y\)

The solution is;

\(x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c\)

\(xy = lny + c\)

Take c = 0, we get;

\(xy = lny\\\\y = e^{xy}\)

Hence, y = e^xy  is an implicit solution of the differential equation

(1-xy)y'=y^2

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Answer:

6.25 hours

Step-by-step explanation:

4 sheep/30 minutes

50 sheep/? minutes

50/4= 12.5

12.5 x 30 min = 375 min

375 min x \(\frac{1hr}{60 min}\) = 6.25 hrs

Answer:

2nd option

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

6xy³z × 3x²yx²

= 6 × 3 × x × x² × x² × y³ × y × z

= 18 × \(x^{(1+2+2)}\) × \(y^{(3+1)}\) × z

= 18\(x^{5}\)\(y^{4}\)z

When subjects are paired or matched in some way, samples are considered to be dependent.

The observations or measurements in one sample are directly related to the observations or measurements in the other sample. Paired samples occur when the same individuals or objects are measured or observed at two different times, under two different conditions, or using two different methods. In a paired design, the subjects are paired or matched based on some characteristic that is expected to influence the outcome of interest. For example, in a study of the effectiveness of a new drug, subjects might be paired based on age, sex, or severity of the disease. By pairing the subjects, the effects of individual differences are reduced, and the statistical power of the analysis is increased. Paired samples are often analyzed using techniques such as the paired t-test or the Wilcoxon signed-rank test.

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Answer:

38.66

Step-by-step explanation:

The circumference of the circle is 12.56 km

From the question, we have the following parameters that can be used in our computation:

Shape = Circle

Radius = 2 km

The circumference of a circle is the perimeter of the circle

i.e. the sum of the units of the arc that surrounds the circle

The circumference equation is represented as

Circumference = 2πr

Substitute the known values in the above equation, so, we have the following representation

Circumference = 2π * 2 km

Evaluate the products in the equation

So, we have

Circumference = 4π km

Substitute π = 3.14

So, we have

Circumference = 4 * 3.14 km

Evaluate

Circumference = 12.56 km

Hence, the circumference is 12.56

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Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

Answer:

15%?

Step-by-step explanation:

sorry if im wrong

According to the given expressions, there was used the multiplication property for inequalities because there's being multiplied the number 61 on both sides.

The daily output achieved by maximum cycle time cannot be calculated by the given information. But, the daily output achieved by minimum cycle time is 1688 units per day (approx).

Given that the line will operate for 450 minutes per day.

The maximum cycle time can be calculated using the formula:

Maximum cycle time = Operating time / Minimum number of cycles

Maximum cycle time = 450 / 1

= 450 minutes

The minimum cycle time can be calculated using the formula:

Minimum cycle time = Operating time / Maximum number of cycles

So,

Minimum cycle time = 450 / (450/20)

= 20 minutes

a. The maximum cycle time is 450 minutes, and the minimum cycle time is 20 minutes.

Maximum cycle time = 450 minutes

Minimum cycle time = 20 minutes

b. The daily output achieved by maximum cycle time can be calculated using the formula:

Daily output = (Operating time * Efficiency) / Cycle time

We know that the operating time is 450 minutes.

Efficiency is not given.

Hence, the daily output cannot be calculated by the given information.The daily output achieved by the minimum cycle time can be calculated using the formula:

Daily output = (Operating time * Efficiency) / Cycle time

Daily output achieved by minimum cycle time = (450 * 75%) / 20

Daily output achieved by minimum cycle time = 1688 units per day (approx)

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Answer:

12

Step-by-step explanation:

4 × 3 = 12

3/3 = 12

2/3 = 8

1/3 = 4

8 slices were eaten and 4 are left, and if you add 8 + 4 or you multiply the 3 × 4, you get 12. There were originally 12 slices.

Answer:

The last two

Step-by-step explanation:

x= 0.6·25

60/100= x/25

Answer: x = 7

Explanation:

Subtract 8 from both sides to isolate x.

x + 8 = 15

x + 8 -8 = 15 - 8

x = 15 - 8

x = 7

Answer:

X=7

Step-by-step explanation:

have a good day /night

The pickup truck travels 19\(\frac{2}{7}\) Miles in gallon.

A unit rate means a rate for one of something.

Given that a pickup truck travels 45 miles on 2\(\frac{1}{3}\) gallons of gas,

Since there are 45 miles in 7/3 gallons

So, 45*3/7 in one gallon = 19\(\frac{2}{7}\) Miles in one gallon

Hence, The pickup truck travels 19\(\frac{2}{7}\) Miles in gallon.

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To solve this problem, let's first understand the information given

   ⇒ says that 150% of expected people showed up

        ⇒ the number of expected people is 340

            ⇒ means 150% of 340 is the number of people who showed up

                ⇒ written mathematically 150% is equivalent to 150/100.

To find the exact number of people we must time 150/100 to 340

   \(\frac{150}{100}*340=1.5 * 340 = 510\)

That means 510 people showed up

Hope that helped!

To get at least JPY 1,324 in exchange for $1,000 U.S. dollars, you would need a conversion rate of at least 1.324 JPY per USD.

The conversion rate represents the value of one currency in terms of another. In this case, we want to determine the conversion rate needed to get at least JPY 1,324 for $1,000 USD. To find the conversion rate, we divide the amount in the foreign currency (JPY) by the amount in the base currency (USD). Therefore, the conversion rate is JPY 1,324 divided by $1,000, which simplifies to 1.324 JPY per USD.

This means that for every U.S. dollar, you would receive at least 1.324 Japanese yen. In practical terms, you would need to find an exchange service or financial institution that offers a conversion rate of 1.324 JPY per USD or better in order to obtain at least JPY 1,324 for $1,000 USD. It's worth noting that exchange rates can fluctuate and may vary between different providers, so it's advisable to check with the specific exchange service for the most accurate and up-to-date conversion rate.

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The equation that represents the given situation of horses and cows will be 2c + 2 = 16.

We have,

A statement that there are 2 more horses than cows in a field.

And,

Total animals in the field = 16,

So,

According to the question,

Let,

Number of cows = c, and Number of horses = h,

So,

As mentioned in the statement above,

We get,

Number of horses = 2 + Number of cows,

i.e.

h = 2 + c     ..... (i)

And,

Total animals in the field = 16,

i.e.

h + c = 16     ..... (ii),

Now,

From equation (i), taking value of h and putting in equation (ii),

We get,

2 + c + c = 16

i.e.

2 + 2c = 16,

So,

The equation that represents the given situation is 2 + 2c = 16.

Hence we can say that the equation that represents the given situation of horses and cows will be 2c + 2 = 16.

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The dimensions of the garden last year were 15 feet by 4 feet.

Let the length of the garden last year be L feet, and the width be W feet. We are given that the area of the garden last year was 60 square feet:

L * W = 60

This year, the garden is 1 foot wider and 3 feet shorter than last year's garden:

Length: L - 3

Width: W + 1

The area of the garden remains the same:

(L - 3) * (W + 1) = 60

Now we have two equations with two variables:

L * W = 60

(L - 3) * (W + 1) = 60

We can solve this system of equations using substitution or elimination. Let's use substitution. From equation 1, we can write L as:

L = 60 / W

Now substitute this expression for L in equation 2:

(60 / W - 3) * (W + 1) = 60

Simplify and solve for W:

60 + 60 / W - 3W - 3 = 60

Combine like terms:

60 / W - 3W = 3

Multiply both sides by W to eliminate the fraction:

60 - 3W² = 3W

Move all terms to one side:

3W² + 3W - 60 = 0

Divide the equation by 3:

W² + W - 20 = 0

Factor the quadratic equation:

(W + 5)(W - 4) = 0

The possible values for W are -5 and 4. However, since width cannot be negative, W must be 4 feet. Now, use the expression for L to find the length:

L = 60 / W = 60 / 4 = 15 feet

So, the dimensions of the garden last year were 15 feet by 4 feet.

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Answer: m= -1/2

Step-by-step explanation:

m is the gradient of a line. and the formula for gradient is (y2-y1)/(x2-x1)

first, find a point on the line, (-2,1) and that is equal to (x1,y1)

then find another point on the line, (2,-1) and that is equal to (x2,y2)

then substitute your points into the formula above and that is equal to

(-1-1)/(2-(-2))

= -2/4

= -1/2

that is your answer

According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

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